Finite Group Databasebeta

← C31×#11560 #21468319

Subgroups — C31×#11560 #21468319

Order 7936.

534 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2534C211yesmaximal, characteristic
2C31×#1466C211yesmaximal, characteristic, complemented
3C31×#1459C211yesmaximal, characteristic, complemented
4C31×#1317C212yesmaximal, complemented
5C31×#1316C212yesmaximal, complemented
6C2×C31×#123C411yescharacteristic
7C2×C31×#120C411yescharacteristic
8C2×C4×D4×C31C2211yescharacteristic
9C22×C22⋊C4×C31C411yescharacteristic
10C31×#432—21no—
11C2×C31×C22⋊C8—21no—
12C31×#396—21no—
13C31×#394—21no—
14C31×#388—21no—
15C31×#386—21no—
16C31×#381C2211yescharacteristic
17C31×#380C411yescharacteristic
18C31×#379C2211yescharacteristic
19C31×#324—21no—
20C31×#323—21no—
21C31×#323C2212yes—
22C31×#323C2212yes—
23C25×C31C2×C411yescharacteristic
24C22×D4×C31—21no—
25C22×D4×C31C2×C411yescharacteristic
26C23×C4×C31C2×C411yescharacteristic
27C23×C4×C31C2×C411yescharacteristic
28C23×C4×C31D411yescharacteristic
29C22×C8×C31—41no—
30C31×#123—42no—
31C31×#120—42no—
32C4×D4×C31—41no—
33C4×D4×C31—41no—
34C2×C4⋊C4×C31—21no—
35C2×C4⋊C4×C31—21no—
36C2×C4⋊C4×C31D411yescharacteristic
37C2×C22⋊C4×C31—21no—
38C2×C22⋊C4×C31—21no—
39C2×C22⋊C4×C31—21no—
40C2×C22⋊C4×C31—21no—
41C2×C22⋊C4×C31—21no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—41no—
44C2×C22⋊C4×C31—41no—
45C2×C22⋊C4×C31C2×C411yescharacteristic
46C2×C22⋊C4×C31C2×C411yescharacteristic
47C2×C22⋊C4×C31D411yescharacteristic
48C2×C22⋊C4×C31C2311yescharacteristic
49C2×C42×C31D411yescharacteristic
50C31×C4⋊C8—41no—
51C31×C22⋊C8—22no—
52C31×C22⋊C8—22no—
53C31×C22⋊C8—41no—
54C31×#97—41no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C24×C31—21no—
59C24×C31—22no—
60C24×C31—41no—
61C24×C31—42no—
62C24×C31—41no—
63C24×C31—81no—
64C24×C31C22⋊C411yescharacteristic
65C24×C31C22×C411yescharacteristic
66C2×D4×C31—22no—
67C2×D4×C31—22no—
68C2×D4×C31—41no—
69C2×D4×C31—42no—
70C2×D4×C31—42no—
71C2×D4×C31—81no—
72C22×C4×C31—21no—
73C22×C4×C31—21no—
74C22×C4×C31—21no—
75C22×C4×C31—21no—
76C22×C4×C31—21no—
77C22×C4×C31—21no—
78C22×C4×C31—21no—
79C22×C4×C31—22no—
80C22×C4×C31—41no—
81C22×C4×C31—41no—
82C22×C4×C31—81no—
83C22×C4×C31—81no—
84C22×C4×C31C22⋊C411yescharacteristic
85C22×C4×C31C22⋊C411yescharacteristic
86C22×C4×C31C22⋊C411yescharacteristic
87C22×C4×C31C2×D411yescharacteristic
88C22×C4×C31C2×D411yescharacteristic
89C2×C8×C31—42no—
90C2×C8×C31—42no—
91C2×C8×C31—82no—
92C4⋊C4×C31—41no—
93C4⋊C4×C31—42no—
94C4⋊C4×C31—81no—
95C22⋊C4×C31—41no—
96C22⋊C4×C31—41no—
97C22⋊C4×C31—42no—
98C22⋊C4×C31—42no—
99C22⋊C4×C31—42no—
100C22⋊C4×C31—42no—
101C22⋊C4×C31—41no—
102C22⋊C4×C31—41no—
103C22⋊C4×C31—41no—
104C22⋊C4×C31—41no—
105C22⋊C4×C31—81no—
106C42×C31—21no—
107C42×C31—21no—
108#11560C3111yesmaximal, characteristic, direct product factor, Sylow
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—21no—
112C23×C31—21no—
113C23×C31—22no—
114C23×C31—41no—
115C23×C31—41no—
116C23×C31—41no—
117C23×C31—41no—
118C23×C31—41no—
119C23×C31—41no—
120C23×C31—41no—
121C23×C31—42no—
122C23×C31—42no—
123C23×C31—41no—
124C23×C31—41no—
125C23×C31—41no—
126C23×C31—82no—
127C23×C31—84no—
128C23×C31—84no—
129C23×C31—82no—
130C23×C31#10012yes—
131C23×C31C2×C22⋊C411yescharacteristic
132C23×C31#13112yes—
133D4×C31—44no—
134D4×C31—84no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—41no—
142C2×C4×C31—42no—
143C2×C4×C31—41no—
144C2×C4×C31—41no—
145C2×C4×C31—41no—
146C2×C4×C31—41no—
147C2×C4×C31—41no—
148C2×C4×C31—41no—
149C2×C4×C31—41no—
150C2×C4×C31—41no—
151C2×C4×C31—41no—
152C2×C4×C31—41no—
153C2×C4×C31—41no—
154C2×C4×C31—41no—
155C2×C4×C31—81no—
156C2×C4×C31—81no—
157C2×C4×C31—81no—
158C2×C4×C31—82no—
159C2×C4×C31#9911yescharacteristic
160C2×C4×C31#9911yescharacteristic
161C8×C31—82no—
162C8×C31—82no—
163#2534C2×C3111yescharacteristic
164#1466C2×C3111yescharacteristic, complemented
165#1459C2×C3111yescharacteristic, complemented
166#1317C2×C3112yescomplemented
167#1316C2×C3112yescomplemented
168C22×C31—21no—
169C22×C31—21no—
170C22×C31—22no—
171C22×C31—22no—
172C22×C31—42no—
173C22×C31—42no—
174C22×C31—42no—
175C22×C31—42no—
176C22×C31—42no—
177C22×C31—41no—
178C22×C31—41no—
179C22×C31—41no—
180C22×C31—41no—
181C22×C31—42no—
182C22×C31—81no—
183C22×C31—81no—
184C22×C31—81no—
185C22×C31—84no—
186C22×C31—84no—
187C22×C31—81no—
188C22×C31—81no—
189C22×C31#40811yescharacteristic
190C22×C31C2×#9911yescharacteristic
191C22×C31C2×#10011yescharacteristic
192C4×C31—21no—
193C4×C31—21no—
194C4×C31—41no—
195C4×C31—41no—
196C4×C31—41no—
197C4×C31—41no—
198C4×C31—81no—
199C4×C31—81no—
200C4×C31—81no—
201C2×#123C4×C3111yescharacteristic
202C2×#120C4×C3111yescharacteristic
203C2×C4×D4C22×C3111yescharacteristic
204C22×C22⋊C4C4×C3111yescharacteristic
205#432—21no—
206C2×C22⋊C8—21no—
207#396—21no—
208#394—21no—
209#388—21no—
210#386—21no—
211#381C22×C3111yescharacteristic
212#380C4×C3111yescharacteristic
213#379C22×C3111yescharacteristic
214#324—21no—
215#323—21no—
216#323C22×C3112yes—
217#323C22×C3112yes—
218C2×C31—21no—
219C2×C31—21no—
220C2×C31—42no—
221C2×C31—42no—
222C2×C31—82no—
223C2×C31#147111yescharacteristic
224C2×C31#212011yescharacteristic
225C2×C31#212111yescharacteristic
226C25C2×C4×C3111yescharacteristic
227C22×D4—21no—
228C22×D4C2×C4×C3111yescharacteristic
229C23×C4C2×C4×C3111yescharacteristic
230C23×C4C2×C4×C3111yescharacteristic
231C23×C4D4×C3111yescharacteristic
232C22×C8—41no—
233#123—42no—
234#120—42no—
235C4×D4—41no—
236C4×D4—41no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4D4×C3111yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—41no—
247C2×C22⋊C4—41no—
248C2×C22⋊C4C2×C4×C3111yescharacteristic
249C2×C22⋊C4C2×C4×C3111yescharacteristic
250C2×C22⋊C4D4×C3111yescharacteristic
251C2×C22⋊C4C23×C3111yescharacteristic
252C2×C42D4×C3111yescharacteristic
253C4⋊C8—41no—
254C22⋊C8—22no—
255C22⋊C8—22no—
256C22⋊C8—41no—
257#97—41no—
258#95—21no—
259#95—21no—
260#95—21no—
261C31#1156011yescharacteristic, direct product factor, Sylow
262C24—21no—
263C24—22no—
264C24—41no—
265C24—42no—
266C24—41no—
267C24—81no—
268C24C22⋊C4×C3111yescharacteristic
269C24C22×C4×C3111yescharacteristic
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—81no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—81no—
287C22×C4—81no—
288C22×C4C22⋊C4×C3111yescharacteristic
289C22×C4C22⋊C4×C3111yescharacteristic
290C22×C4C22⋊C4×C3111yescharacteristic
291C22×C4C2×D4×C3111yescharacteristic
292C22×C4C2×D4×C3111yescharacteristic
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—82no—
296C4⋊C4—41no—
297C4⋊C4—42no—
298C4⋊C4—81no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—42no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—81no—
310C42—21no—
311C42—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—22no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—42no—
325C23—42no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—82no—
330C23—84no—
331C23—84no—
332C23—82no—
333C23C31×#10012yes—
334C23C2×C22⋊C4×C3111yescharacteristic
335C23C31×#13112yes—
336D4—44no—
337D4—84no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—82no—
362C2×C4C31×#9911yescharacteristic
363C2×C4C31×#9911yescharacteristic
364C8—82no—
365C8—82no—
366C22—21no—
367C22—21no—
368C22—22no—
369C22—22no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—42no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—84no—
384C22—84no—
385C22—81no—
386C22—81no—
387C22C31×#40811yescharacteristic
388C22C2×C31×#9911yescharacteristic
389C22C2×C31×#10011yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—81no—
397C4—81no—
398C4—81no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—42no—
403C2—82no—
404C2C31×#147111yescharacteristic
405C2C31×#212011yescharacteristic
406C2C31×#212111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#99
commutatorC24C22×C4×C31
Frattini, cosocleC2×C22⋊C4C23×C31
prime radicalC2×C31×#120C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C31×#1466C2semidirect
3. C31×#1459C2semidirect
4. C31×#1317C2semidirect
5. C31×#1316C2semidirect
108. #11560C31direct (N × H)
164. #1466C2×C31semidirect
165. #1459C2×C31semidirect
166. #1317C2×C31semidirect
167. #1316C2×C31semidirect
261. C31#11560direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C31×#25342
C31×#14662
C31×#14592
C31×#13172
C31×#13162
#1156031